摘要：In this paper, we give an affirmative answer to the following question: Is the solvability of some nonlinear dynamic equations on a time scale T $\mathbb{T}$ not only sufficient but in a certain sense also necessary for the validity of some dynamic Hardy-type inequalities with two different weights? In fact, this answer will give a new characterization of the weights in a weighted Hardy-type inequality on time scales. The results contain the results when T = R $\mathbb{T}=\mathbb{R}$ , T = N $\mathbb{T}=\mathbb{N}$ , and when T = q N 0 $\mathbb{T}=q^{\mathbb{N}_(}$ as special cases. Some applications are given for illustrations.
关键词：Hardy’s inequality ; Dynamic equations ; Time scales
